Reduced-rank filtering is a common method for attenuating noise in seismic data. Because conventional reduced-rank filtering distinguishes signals from noises only according to singular values, it performs poorly when the signal-to-noise ratio (S/N) is very low or when data contain high levels of isolate or coherent noise. Therefore, we have developed a novel and robust reduced-rank filtering method based on singular value decomposition in the time-space domain. In this method, noise is recognized and attenuated according to the characteristics of the singular values and the singular vectors. The left and right singular vectors corresponding to large singular values are selected first. Then, the right singular vectors are classified into different categories according to their curve characteristics, such as jump, pulse, and smooth. Each kind of right singular vector is related to a type of noise or seismic event, and it is corrected by using a different filtering technology, such as mean filtering, edge-preserving smoothing, or edge-preserving median filtering. The left singular vectors are also corrected by using the filtering methods based on frequency attributes such as main frequency and frequency bandwidth. To process seismic data containing a variety of events, local data are extracted along the local dip of the event. The optimal local dip is identified according to the singular values and singular vectors of the data matrices that are extracted along different trial directions. This new filtering method has been applied to synthetic and field seismic data, and its performance is compared with that of several conventional filtering methods. The results indicate that the new method is more robust for data with a low S/N, strong isolated noise, or coherent noise. The new method also overcomes the difficulties associated with selecting an optimal rank.

中文翻译：

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低信噪比地震数据的鲁棒奇异值分解滤波

降秩滤波是用于衰减地震数据中噪声的常用方法。由于常规的降秩滤波仅根据奇异值将信号与噪声区分开，因此当信噪比（S / N）非常低或数据包含高水平的隔离噪声或相干噪声时，其性能较差。因此，我们在时空域中基于奇异值分解开发了一种新颖且健壮的降秩滤波方法。在这种方法中，根据奇异值和奇异矢量的特征来识别和衰减噪声。首先选择与大奇异值相对应的左右奇异矢量。然后，将右奇异矢量根据其曲线特性（例如跳跃，脉冲和平滑度）分类为不同类别。每种正确的奇异矢量都与一种噪声或地震事件有关，并且可以通过使用其他滤波技术（例如均值滤波，保留边缘的平滑或保留边缘的中值滤波）进行校正。还使用基于频率属性（例如主频率和频率带宽）的滤波方法对左奇异矢量进行校正。为了处理包含各种事件的地震数据，沿着事件的局部倾角提取局部数据。根据沿不同试验方向提取的数据矩阵的奇异值和奇异矢量，确定最佳局部下陷。这种新的滤波方法已应用于合成和野外地震数据，并将其性能与几种常规滤波方法进行了比较。结果表明，该新方法对于具有低S / N，强隔离噪声或相干噪声的数据更健壮。新方法还克服了与选择最佳等级相关的困难。